2019-10-09
10:15 at HCP F 43.4

Thermodynamic modeling of polymer solutions accounting for jumps between classes of molecular conformations

Mohsen Talebi

Polymer Physics, Department of Materials, ETH Zurich

Back in 1997 and 1999, remarkable observations in the group of Steven Chu suggested that, under strong flow regimes (shear or elongational), the non-equilibrium state of a long lambda-DNA molecule can be categorized in configuration classes like dumbbell, half-dumbbell, kink, and fold. This idea of classification of the non-equilibrium state of the polymer was called molecular individualism by P. G. de Gennes. Later on, there has been an attempt in the work [1] to use this idea to provide a configuration-based model for simulation of dilute polymer solutions under different types of flows. Inspired by this work, the main aim of our project is to provide an admissible thermodynamic configuration-based model for these solutions in the framework of the GENERIC thermodynamic structures. We model each class by an elastic dumbbell with beads connected by a general entropic spring. We also consider the specific cases of Hookean and FENE-P springs. In our model, we have chosen three state variables for the total hydrodynamic fields, a conformation-tensor field for each configuration class, and concentration fields as the population of each class. According to GENERIC, the evolution of the system is separated into reversible and irreversible parts. The reversible evolution is described by Poisson structures. In our case, we are considering Poisson structures associated with the convection processes of scalar density, vector density, and tensor fields. The irreversible evolution equations may be described by a friction matrix or a dissipation potential. In our problem, we are using them together based on the approach of the work [2]. The first irreversible process that we consider is the jump between configuration classes which is described by the dissipation potential of chemical reactions. Inside each class, we assign a friction matrix for the relaxation process of conformation tensors. Moreover, we need to consider a friction matrix for the diffusion process of polymers in each class. In the end, as the result of this modeling, we obtain the evolution equations of all state variables. The last goal of the project is to compare the evolution of the state variables derived from the model with the evolution inferred from direct numerical simulation of the microscopic dynamics of the polymer. We start moving toward this goal by adopting the classification algorithm introduced in the work [3] to categorize the instantaneous state of a bead-spring model with worm-like-chain springs. The criteria used in this algorithm try to mimic the experimental criteria introduced in the experiments of the group of S. Chu to sort the polymer into the classes coil, fold, dumbbell, half-dumbbell, kink, and stretched. We will present the implementation of this method for a single polymer experiencing a shear flow.

[1] V. Venkataramani, R. Sureshkumar, and B. Khomami. Coarse-grained modeling of macromolecular solutions using a configuration-based approach. Journal of Rheology, 52(5):1143-1177, 2008.
[2] H. C. Öttinger. On the combined use of friction matrices and dissipation potentials in thermodynamic modeling. Journal of NonEquilibrium Thermodynamics, 44(3):295-302, 2019.
[3] R. G. Larson, H. Hu, D. E. Smith, and S. Chu. Brownian dynamics simulations of a DNA molecule in an extensional flow field. Journal of Rheology, 43(2):267-304, 1999.